# Showing papers in "IEEE Transactions on Circuit Theory in 1969"

••

TL;DR: In this paper, the authors derived a related adjoint network representation and sensitivity coefficients for networks containing a very broad class of elements: those that admit a parametric representation, and a brief discussion is given as to how these results may be exploited in a general automated network design scheme.

Abstract: It has been established that the adjoint network and network sensitivities play important roles in automated network design algorithms. The present paper derives a related adjoint network representation and sensitivity coefficients for networks containing a very broad class of elements: those that admit a parametric representation. A brief discussion is given as to how these results may be exploited in a general automated network design scheme.

503 citations

••

223 citations

••

TL;DR: This work considers the problem of designing a network which satisfies a prespecified survivability criterion with minimum cost, and a heuristic approach is described, based on recent work on the traveling salesman problem, which leads to a practical design method.

Abstract: We consider the problem of designing a network which satisfies a prespecified survivability criterion with minimum cost. The survivability criterion demands that there be at least r_{ij} node disjoint paths between nodes i and j , where (r_{ij}) is a given redundancy requirement matrix. This design problem appears to be at least as difficult as the traveling salesman problem, and present techniques cannot provide a computationally feasible exact solution. A heuristic approach is described, based on recent work on the traveling salesman problem, which leads to a practical design method. Algorithms are described for generating starting networks, for producing local improvements in given networks, and for testing the redundancy of networks at each stage. This leads to networks which are locally optimum with respect to the given transformation. Randomizing the starting solution ensures that the solution space is widely sampled. Two theorems are given which allow great reduction in the amount of computation required to test the redundancy of a network. Finally, some design examples are given.

212 citations

••

TL;DR: The reinterpretation of this sensitivity of any associated network function with respect to scalar indices of network performance provides an automated frequency-domain network design principle of far-reaching consquences.

Abstract: Application of Tellegen's theorem to an originally specified network leads to a simple computation of the unnormalized sensitivity of any associated network function with respect to all pertinent network parameters in terms of analysis of it and its topologically equivalent adjoint network. The reinterpretation of this sensitivity to scalar indices of network performance provides an automated frequency-domain network design principle of far-reaching consquences. A computer program has been written to implement the design algorithm. Preliminary results show this program to be highly effective.

202 citations

••

TL;DR: In this paper, the problem of decomposing a network into different groups of electrical components, which are interconnected by the minimum number of leads, is discussed, and minimal groups of components are defined as the ones fulfilling a chosen minimality criterion.

Abstract: The problem of decomposing a network into different groups of electrical components, which are interconnected by the minimum number of leads, is discussed. For this purpose, minimal groups of components are defined as the ones fulfilling a chosen minimality criterion, and a number of their properties are illustrated. Some of these properties are directly employed in a procedure for the determination of all the minimal groups for a given network.

77 citations

••

NEC

^{1}TL;DR: In this article, the state-variable analysis of the most general class of lumped time-invariant RLC networks is discussed in connection with the mixed analysis of networks.

Abstract: This paper deals with the state-variable analysis of the most general class of lumped time-invariant RLC networks. The hybrid descriptions of coupled elements are discussed in connection with the mixed analysis of networks. Sufficient conditions for the uniqueness of solutions of coupled resistor networks and RLC networks are given in terms of hybrid descriptions. The set of state variables are taken so that the order of state equations coincides with the number of finite natural frequencies in the linear case. A simple method for determining such a set of state variables by means of two particular trees, C -normal tree and L - normal tree, is also presented. The standard form of state equations are represented by means of a signal flow graph.

75 citations

••

62 citations

••

TL;DR: In this article, the use of state-space techniques and Routh's algorithm was used for performing the continued fraction inversion. But this method is not suitable for the case of polynomials.

Abstract: The operation of converting a continued fraction into a rational transfer function of two polynomials is tedious. By the use of state-space techniques and Routh's algorithm, a new method is established for performing the continued fraction inversion.

51 citations

••

TL;DR: In this paper, a pair of trees of a graph is said to be maximally distant if the distance between these trees is maximum in the graph, and the principal partition of the graph is uniquely determined for the graph.

Abstract: A pair of trees of a graph is said to be maximally distant if the distance between these trees is maximum in the graph Necessary and sufficient conditions for maximally distant trees are presented Fundamental properties of the maximally distant trees provide us with the principal partition of a graph that is uniquely determined for the graph Some useful properties of the principal partition, together with the application to the classification of the trees, are discussed

50 citations

••

TL;DR: In this article, it was shown that the familiar least square/Taylor technique may be generalized into a least p th/Taylor method, which is only slightly more complicated if p > 2; then the maximum error is smaller than for p = 2 and convergence often improves.

Abstract: It is shown that the familiar least-squares/Taylor technique may easily be generalized into a least p th/Taylor method. The process is only slightly more complicated if p > 2; then the maximum error is smaller than for p = 2 and the convergence often improves.

49 citations

••

••

TL;DR: It is shown that this class is the most general class of time-varying filters that preserve the wide-sense stationarity of the inputs and that such properties can facilitate considerably the analysis of systems incorporating these filters.

Abstract: Discrete-time signals and digital filters have become increasingly important in recent years with the rapid advance of technology in integrated digital circuitry and the increasing availability of digital computers. This paper is concerned with a class of linear time-varying digital filters and the response of such filters with stochastic input signal. It is shown that these filters possess a number of useful properties; the most important of which is the preservation of wide-sense stationarity of stochastic inputs. Such properties can facilitate considerably the analysis of systems incorporating these filters. It is shown that this class is the most general class of time-varying filters that preserve the wide-sense stationarity of the inputs. A subclass of these filters is shown to be periodic and hence can be implemented simply by using parallel connection of time-invariant filters and a rotating switch. The response of these filters to periodic inputs is analyzed.

••

TL;DR: In this article, a theory for two-port generalized interdigital networks is presented and necessary and sufficient conditions for the individual realization of any admittance parameter of such a network are presented.

Abstract: A theory for two-port generalized interdigital networks is presented Initially, after the definition of an arbitrary generalized interdigital network, properties of admittance scaling and transformations of general interdigital lines are formulated The necessary and sufficient conditions are then presented for the individual realization of any admittance parameter of such a network The results obtained in this section influence the choice of a compact set of sufficiency conditions for the realization of any arbitrary twoport admittance matrix by this class of networks These sufficiency conditions are also shown to imply simple sufficiency conditions on the insertion-loss function of a resistively terminated, two-port generalized interdigital network

••

TL;DR: State equations such that the state vector is composed exclusively of currents in inductances and voltages across capacitances can be obtained by algebraic methods.

Abstract: State equations such that the state vector is composed exclusively of currents in inductances and voltages across capacitances have been obtained in the past by topological methods. The same result as well as an extension thereof to general finite lumped constant linear systems can be achieved by algebraic methods. The only requirement is that these systems are well defined, i.e., such that they represent a meaningful model of an actual physical system.

••

TL;DR: In this paper, all the poles and zeros of the transfer function of a linear time-invariant single-input single-output (SISO) system were determined by finding the eigenvalues of a matrix obtained from the state and output equations of the system.

Abstract: This paper is concerned with techniques for the determination of all the critical frequencies (i.e., all the poles and zeros) of the transfer function of a linear time-invariant singleinput single-output system. Unlike methods involving the computation of polynomial coefficients, the techniques presented find the transfer zeros as the eigenvalues of a matrix obtained from the state and output equations of the system. A computational assessment is given with illustrative examples. In particular, the computation of actual bounds on the critical frequencies is discussed, and the application of these techniques to frequency analysis of networks is considered. Preliminary computer test results have confirmed that they require significantly less computation time and admit the possibility of detailed roundoff error analysis.

••

TL;DR: The synthesis methods developed here allow the designer to choose a single type of adjustable building block for each independent real variable; to maintain control of the functional complexity of these adjustable blocks; and to use, in the single real variable case, only the absolute minimum number of such adjustable blocks.

Abstract: The synthesis of the class of adjustable networks that respond or adapt to an independent (with respect to frequency) real variable, or several such independent real variables, and that respond as linear time-invariant networks for fixed values of these variables, is considered. Thus, for general networks in this class, the network functions (possibly after some frequency transformations) are real and rational in (possibly) several frequency variables, and the coefficients of the numerator and denominator polynomials in the several frequency variables are real functions of the real independent variables. An objection to most synthesis procedures for adjustable networks is that the adjustable elements used, whether passive or active, have had to be assumed to be highly versatile in their functional form. Practically, however, such adjustable elements may not exist. Also, synthesis procedures that use more than one type of adjustable elements for each independent real variable may result in a serious tracking problem. The synthesis methods developed here allow the designer 1) to choose a single type of adjustable building block for each independent real variable; 2) to maintain control of the functional complexity of these adjustable blocks; and 3) to use, in the single real variable case, only the absolute minimum number of such adjustable blocks.

••

TL;DR: The distinguishability criteria in directed graphs is developed and bounds on the number of test points needed to locate faults in a sequential system are derived.

Abstract: Discrete sequential systems like the functional elements of a digital computer can be represented by directed graphs. In this paper we study an application of graph theory to computer diagnosis. Specifically, we develop the distinguishability criteria in directed graphs and derive bounds on the number of test points needed to locate faults in a sequential system.

••

••

TL;DR: In this article, a state-space approach is used to derive an exact closed-form solution for the steady-state and transient response of a general commutated network terminated in a multiport.

Abstract: A state-space approach is used to derive an exact closed-form solution for the steady-state and transient response of a general commutated network terminated in a multiport. By expanding the time-varying transfer function N(p, t) in a Fourier series, the transfer function at input frequency N_{0}(p) , and the transfer functions at harmonic frequencies N_{m}(p) are then calculated. A necessary and sufficient condition for the recovery of the input signal, without distortion due to the harmonics, is given. From the general analysis, we immediately obtain previously available results on comb filters, n -path filters, sample-data filters, etc., as special cases. The resulting closed-form solutions in terms of element values are most suitable for computer simulation in which the performance of the commutated network is to be evaluated as the element values are varied.

••

••

TL;DR: In this article, a systematic method is described for deriving exact closed-form solutions of the telegrapher's equation in terms of standard transcendental functions, which yields far more general profiles for Z(x), Y(x), or Z(ex)/ Y(ex) than previously given.

Abstract: A proliferation of exact closed-form solutions of the telegrapher's equation V_{xx} - Z_{x}Z^{-1}V_{x} - kZ Y V = 0 for the voltage V(x) in an RC or lossless transmission line, with distributed series impedance Z(x) and shunt admittance Y(x) , respectively, have emerged in recent years. Generalizations of known solutions have been constructed, sometimes using ad hoc methods. A systematic method is described for deriving exact solutions in terms of standard transcendental functions, which yields far more general profiles for Z(x), Y(x) , or Z(x)/ Y(x) than previously given. Examples of the procedure are given based upon Bessel's, Whittaker's, and the hypergeometric equation, and previously derived profiles emerge as special cases of the analysis.

••

••

••

TL;DR: The pole-zero frequencies and phase deviations of four-, six-, and eight-pole broad-band 90° phase-difference networks are derived by algebraic means and the results agree with those obtained by elliptic functions but lead to simpler computer solutions.

Abstract: The pole-zero frequencies and phase deviations of four-, six-, and eight-pole broad-band 90° phase-difference networks are derived by algebraic means. The results agree with those obtained by elliptic functions but lead to simpler computer solutions. An RC design method based on a bridge circuit is developed. The conditions for minimum loss, maximum stability, and minimum number of circuit elements are stated for unterminated and terminated network pairs. Computer methods for obtaining network component values and circuit characteristics are described. A timesharing computer program is available for four-, six-, and eightpole networks and all frequency ranges.

••

TL;DR: In this article, the synthesis of simultaneously prescribed drivingpoint and transfer admittances for distributed RC networks without transformers is considered, and the realizations given, in general, involve an arbitrary multiplying constant for the transfer admittance and are valid except when the prescribed transmission zeros, t = \tanh \sqrt{p} = \delta 0 + j \omega 0, are such that

Abstract: The synthesis of simultaneously prescribed drivingpoint and transfer admittances for distributed RC networks without transformers is considered. Realizations with common ground connections are required. The realizations given, in general, involve an arbitrary multiplying constant for the transfer admittance and are valid except when the prescribed transmission zeros, t = \tanh \sqrt{p} = \delta_{0} + j \omega_{0} are such that \omega_{0}^{2} \delta_{0}^{2} 1 + \omega_{0}^{2} . If only the short-circuit transfer admittance y_{12} or the open-circuit voltage transfer ratio T_{12} is specified, a realization using surplus factors is given valid for all transmission zeros other than real zeros less than unity, which can never be realized by an unbalanced commensurate distributed RC network, and that for such networks, zeros of transmission where \delta_{0}^{2} >\omega_{0}^{2} + (\delta_{0}^{2} + \omega_{0}^{2})^{2} always require the use of surplus factors. Examples of the various synthesis procedures are given.

••

TL;DR: A computer algorithm is described in this paper that computes the dc solution of first-order differential equations that characterize networks containing transistors, diodes, capacitors, inductors, resistors, and voltage sources with neither cut sets nor closed loops of either junctions, capacitor, or inductors.

Abstract: The dc state vector is often the desired initial condition for the solution of a system of first-order differential equations that characterize network dynamics. A computer algorithm is described in this paper that computes the dc solution of first-order differential equations that characterize networks containing transistors, diodes, capacitors, inductors, resistors, and voltage sources with neither cut sets nor closed loops of either junctions, capacitors, or inductors. Networks containing current sources were not considered. The Newton-Raphson iteration function is the basis of the dc solution algorithm. The unique feature of the solution procedure is the use of upper bounds on the solution to avoid slow convergence and difficulties in computing exponential functions. Derivation of the upper solution bounds is discussed in detail.

••

••

TL;DR: An effective computational algorithm for the design of resistance n -port networks from given n \times n real, symmetric admittance or impedance matrix specifications is derived and discussed.

Abstract: An effective computational algorithm for the design of resistance n -port networks from given n \times n real, symmetric admittance or impedance matrix specifications is derived and discussed. The computer program that results from this algorithm not only realizes realizable admittance or impedance matrices, but also usually indicates nonrealizability and always provides a "best approximation" in such situations.